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Class of problems for PDEs
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface
Cauchy_problem
Existence and uniqueness theorem for certain partial differential equations
differential equations associated with Cauchy initial value problems. A special case was proven by Augustin Cauchy (1842), and the full result by Sofya
Cauchy–Kovalevskaya_theorem
u(t)} of the Cauchy problem ( u ( 0 ) = u 0 {\displaystyle u(0)=u_{0}} ) at the moment of time t > 0 {\displaystyle t>0} . If the Cauchy problem is well posed
Abstract differential equation
Abstract_differential_equation
French mathematician (1789–1857)
momentum equation Cauchy–Peano theorem Cauchy principal value Cauchy problem Cauchy product Cauchy's radical test Cauchy–Rassias stability Cauchy–Riemann equations
Augustin-Louis_Cauchy
Property of vector fields in mathematics
important problem in the theory of partial differential equations is to determine sufficient conditions on the vector fields Ai for the Cauchy problem { ∂ u
Hörmander's_condition
Generalization of the exponential function
a unique classical solution of the Cauchy problem. When these assertions hold, the solution of the Cauchy problem is given by u ( t ) ∈ T ( t ) x {\textstyle
C0-semigroup
Null hypersurface in general relativity
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory
Cauchy_horizon
Property of differential equations describing physical phenomena
many results on this topic. For example, the Cauchy–Kowalevski theorem for Cauchy initial value problems essentially states that if the terms in a partial
Well-posed_problem
Proposal in harmonic analysis
{R} ^{n})} that was both necessary and sufficient for the associated Cauchy problem. Sigeru Mizohata noticed that Takeuchi’s argument was not compelling
Mizohata–Takeuchi_conjecture
Submanifold of Lorentzian manifold
named for French mathematician Augustin-Louis Cauchy (1789–1857) due to their relevance for the Cauchy problem of general relativity. Although it is usually
Cauchy_surface
Principle suggesting that time travel paradoxes are inherently impossible
would be permitted. In a 1990 paper by Novikov and several others, "Cauchy problem in spacetimes with closed timelike curves", the authors state: The only
Novikov self-consistency principle
Novikov_self-consistency_principle
Effect in physics
conserved. The rigorous mathematical theory is based on solving the Cauchy problem for the evolution equation (here the partial differential Vlasov–Poisson
Landau_damping
theorem Cauchy matrix (and Cauchy determinant) Cauchy net Cauchy–Peano theorem Cauchy point Cauchy principal value Cauchy problem Abstract Cauchy problem Cauchy
List of things named after Augustin-Louis Cauchy
List_of_things_named_after_Augustin-Louis_Cauchy
usually forms a finite-dimensional Lie algebra. The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential
Mathematics of general relativity
Mathematics_of_general_relativity
Mathematical inequality relating inner products and norms
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between
Cauchy–Schwarz_inequality
Existence and uniqueness of solutions to initial value problems
under which an initial value problem has a unique solution. It is also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence
Picard–Lindelöf_theorem
Type of calculus problem
the initial value problem. Thus, this is an example of such a problem with infinite number of solutions. Also called a Cauchy problem by some authors.[citation
Initial_value_problem
American computer scientist and mathematician (born 1941)
mathematics from Brandeis University. His dissertation, The analytic Cauchy problem with singular data, is about singularities in analytic partial differential
Leslie_Lamport
Boundary-value problem in differential equations
In mathematics, a Cauchy (French: [koʃi]) boundary condition augments an ordinary differential equation or a partial differential equation with conditions
Cauchy_boundary_condition
Generalized function whose value is zero everywhere except at zero
below), rather than in the sense of measures. Another example is the Cauchy problem for the wave equation in R1+1: c − 2 ∂ 2 u ∂ t 2 − Δ u = 0 u = 0 , ∂
Dirac_delta_function
PDE to describe nonlinear wave motion
corresponding Cauchy problems share an intriguing and complex mathematical relationship. Aguilar et al. proved that the solution of the Cauchy problem for the
Kadomtsev–Petviashvili equation
Kadomtsev–Petviashvili_equation
Partial differential equations with data on two intersecting characteristics
issuing from a common point. The problem is named after Édouard Goursat and is closely related to the Cauchy problem. For the second-order hyperbolic
Goursat_problem
Type of differential equation
boundary condition Neumann boundary condition Robin boundary condition Cauchy problem Various topics Jet bundle Laplace transform applied to differential
Partial_differential_equation
Type of partial differential equations
well-posed initial value problem for the first n − 1 {\displaystyle n-1} derivatives.[citation needed] More precisely, the Cauchy problem can be locally solved
Hyperbolic partial differential equation
Hyperbolic_partial_differential_equation
Probability distribution
The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as
Cauchy_distribution
Method for solving partial differential equations
possible to go from solutions of the Cauchy problem (or initial value problem) to solutions of the inhomogeneous problem. Consider, for instance, the example
Duhamel's_principle
Type of problem involving ODEs or PDEs
is a Cauchy boundary condition. A type 0 boundary condition has no physical boundary. Aside from the boundary condition, boundary value problems are also
Boundary_value_problem
Physics problem related to laws of motion and gravity
of L) in the complex plane centered around the real axis (related to the Cauchy–Kovalevskaya theorem). Find a conformal transformation that maps this strip
Three-body_problem
French mathematical physicist (1923–2025)
introduced the notion of maximal Cauchy development, important in the study of global aspects of the Cauchy problem in general relativity and the theorems
Yvonne_Choquet-Bruhat
Differential equation that is linear with respect to the unknown function
unknowns c1 and c2. Solving this system gives the solution for a so-called Cauchy problem, in which the values at 0 for the solution of the DEQ and its derivative
Linear_differential_equation
American physicist, writer, and Nobel Laureate (born 1940)
Thorne, K. S. and Yurtsever, U., Physical Review D., 1990, (in press), Cauchy Problem in Spacetimes with Closed Timelike Curves. Kip S. Thorne (1994). Black
Kip_Thorne
Mathematical problems related to differential equations
Cauchy problems for 1+1 dimensional partial differential equations on the line, or to periodic problems, or even to initial-boundary value problems (Fokas
Riemann–Hilbert_problem
Hypothetical travel into the past or future
Echeverria; Gunnar Klinkhammer; Kip Thorne; Ulvi Yurtsever (1990). "Cauchy problem in spacetimes with closed timelike curves". Physical Review D. 42 (6):
Time_travel
Topics referred to by the same term
format Child process, Computing process created by another process Cauchy problem, in partial differential equations Complex projective space (CPn), the
CP
Theoretical paradox resulting from time travel
Fernando; Klinkhammer, Gunnar; Thorne, Kip S.; Yurtsever, Ulvi (1990). "Cauchy problem in spacetimes with closed timelike curves". Physical Review D. 42 (6):
Temporal_paradox
Characteristic property of holomorphic functions
In mathematics, the Cauchy–Riemann equations are two partial differential equations that characterize differentiability of complex functions. The equations
Cauchy–Riemann_equations
Theorem regarding the existence of a solution to a differential equation
Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees
Peano_existence_theorem
Partial differential equation describing the evolution of temperature in a region
usually possible to consider the associated abstract Cauchy problem and show that it is a well-posed problem and/or to show some qualitative properties (like
Heat_equation
Physics of the cause–effect relation
determinism in mathematical models as dealt with in the mathematical Cauchy problem. Confusion between causality and determinism is particularly acute in
Causality_(physics)
Hypothetical faster-than-light particle
superluminally. However, such theories, in general, do not have a well-defined Cauchy problem (for reasons related to the issues of causality discussed above), and
Tachyon
Argentine mathematician
equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón's
Alberto_Calderón
Real function with finite total variation
the paper (Conway & Smoller 1966), proving that the solution of the Cauchy problem for such equations is a function of bounded variation, provided the
Bounded_variation
Metric geometry
mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively
Complete_metric_space
Representation of mechanical stress at every point within a deformed 3D object
continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress
Cauchy_stress_tensor
Boundary in spacetime satisfying given conditions
horizon, a surface defined in general relativity Cauchy horizon, a surface found in the study of Cauchy problems Cosmological horizon, a limit of observability
Horizon_(general_relativity)
Concept of complex analysis
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions
Residue_theorem
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
Equation
The Cauchy momentum equation is a vector partial differential equation put forth by Augustin-Louis Cauchy that describes the non-relativistic momentum
Cauchy_momentum_equation
Theory of gravitation as curved spacetime
1082158, PMID 12624255, S2CID 119368762 Bruhat, Yvonne (1962), "The Cauchy Problem", in Witten, Louis (ed.), Gravitation: An Introduction to Current Research
General_relativity
Russian mathematician (born 1961)
in 1931) on the uniqueness of the solution to the Cauchy problem: it is shown that the Cauchy problem with a unit diffusion coefficient and locally bounded
Vladimir_Bogachev
Yang–Mills coupled to a Higgs field
geometric setting. M.V. Goganov and L.V. Kapitanskii have shown that the Cauchy problem for hyperbolic Yang–Mills–Higgs equations in Hamiltonian gauge on 4-dimensional
Yang–Mills–Higgs_equations
Equation known for chaotic behavior
and Δ 2 {\displaystyle \Delta ^{2}} is the biharmonic operator. The Cauchy problem for the 1d Kuramoto–Sivashinsky equation is well-posed in the sense
Kuramoto–Sivashinsky_equation
Soviet, Canadian mathematician
Cauchy problem for weakly hyperbolic equations. In particular he discovered a necessary (later proven to be sufficient) condition for Cauchy problem to
Victor_Ivrii
Yvonne Choquet-Bruhat and Robert Geroch discuss global aspects of the Cauchy problem in general relativity. 1965-70 – Subrahmanyan Chandrasekhar and colleagues
Timeline of gravitational physics and relativity
Timeline_of_gravitational_physics_and_relativity
Problem of solving a partial differential equation subject to prescribed boundary values
of PDE problems defined by the information given at the boundary, including Neumann problems and Cauchy problems. Consider the Dirichlet problem for the
Dirichlet_problem
Group of differential equations
x_{k}}}-{\frac {\partial f_{k}}{\partial x_{i}}}=0,1\leq i,k\leq m.} See also: Cauchy problem and Ehrenpreis's fundamental principle. A system is considered nonlinear
System of differential equations
System_of_differential_equations
Concept in complex analysis
first paper where a sufficient condition for the solvability of the Cauchy problem for holomorphic functions of several complex variables is given. Osgood
Wirtinger_derivatives
Spacetime manifold
was introduced by Leray in order to consider well-posedness of the Cauchy problem for the wave equation on the manifold. In 1970 Geroch proved the equivalence
Globally_hyperbolic_spacetime
Armenian mathematician
doctoral degree (Russian doctorate beyond the Ph.D.) with the thesis Cauchy Problem for Weakly Hyperbolic Equations from the Institute of Mathematics at
Anry_Nersessian
solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution at some
Singular_solution
Theorem in mathematics
value theorem in its modern form was stated and proved by Augustin Louis Cauchy in 1823. Many variations of this theorem have been proved since then. Let
Mean_value_theorem
(^{*})} with x < x 0 {\displaystyle x<x_{0}} . Consider the initial value Cauchy problem for a single equation of the first order: y ′ = f ( x , y ) , ( x ,
Chaplygin's Theorem and Method for Solving ODE
Chaplygin's_Theorem_and_Method_for_Solving_ODE
Continuous wavelets
In mathematics, Cauchy wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The Cauchy wavelet of order p {\displaystyle
Cauchy_wavelet
ISBN 978-0-521-09893-9. OCLC 1499723. Copson, E. T. (1956-06-12). "On a regular Cauchy problem for the Euler—Poisson—Darboux equation". Proc. R. Soc. Lond. A. 235
Euler–Poisson–Darboux equation
Euler–Poisson–Darboux_equation
French mathematician (1865–1963)
1896, pp. 199–220 Online Hadamard, Jacques (2003) [1923]. Lectures on Cauchy's problem in linear partial differential equations. Dover Phoenix editions. Dover
Jacques_Hadamard
Problem in differential geometry
Möbius strip. A unique solution always exists. It can be viewed as a Cauchy problem for minimal surfaces, allowing one to find a surface if a geodesic,
Björling_problem
French-Tunisian mathematician
Alinhac, with a thesis entitled Uniqueness and non-uniqueness of the Cauchy problem for real symbol operators. Then she devoted herself to research at École
Hajer_Bahouri
Awarded every year by the American Mathematical Society
ISSN 0273-0979. Calderón, A. P. (1958). "Uniqueness in the Cauchy problem for partial differential equations". American Journal of Mathematics
Leroy_P._Steele_Prize
Equation of statistical mechanics
(VHC Inc.) 0-89573-752-3. DiPerna, R. J.; Lions, P. L. (1989). "On the Cauchy Problem for Boltzmann Equations: Global Existence and Weak Stability". Annals
Boltzmann_equation
Physical quantity that expresses internal forces in a continuous material
equilibrium and calculus of infinitesimals. With those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model of a
Stress_(mechanics)
Time travel using quantum mechanics
Klinkhammer, Gunnar; Thorne, Kip; Yurtsever, Ulvi (15 September 1990). "Cauchy problem in spacetimes with closed timelike curves" (PDF). Physical Review. 42
Quantum mechanics of time travel
Quantum_mechanics_of_time_travel
French mathematician (born 1956)
ISBN 978-1-4704-2558-6. MR 3443169. Zbl 1342.35002. Glassey, Robert T. (1996). The Cauchy problem in kinetic theory. Philadelphia, PA: Society for Industrial and Applied
Pierre-Louis_Lions
Belgian mathematician (1954–2018)
"Nonlinear partial differential equations and applications: On the global Cauchy problem for the nonlinear Schrödinger equation". Proceedings of the National
Jean_Bourgain
Japanese mathematician
initial value problem. I. Arch. Rational Mech. Anal. 16 (1964), 269–315. Hiroshi Fujita. On the blowing up of solutions of the Cauchy problem for ut = Δu
Hiroshi_Fujita
Matrices satisfying a differential equation
s)^{-1},} where U ( t , s ) {\displaystyle U(t,s)} is the solution of the Cauchy problem d d t U ( t , s ) = P ( t ) U ( t , s ) , U ( s , s ) = I , {\displaystyle
Lax_pair
Soviet and Ukrainian mathematician
value problem as well as the Cauchy problem for system of linear partial differential equations. In her studies, translated from Russian, in the Cauchy problem
Valentina_Borok
Japanese mathematician (1924–2002)
observation Mizohata made on some work of Jiro Takeuchi related to the Cauchy problem evolved into the Mizohata-Takeuchi conjecture, to which Hannah Cairo
Sigeru_Mizohata
Numerical method
PDE problem is well-posed as an initial value (Cauchy) problem in at least one dimension, because ODE and DAE integrators are initial value problem (IVP)
Method_of_lines
Sumset of a field subject to a specific polynomial restriction
{\displaystyle P(a_{1},\ldots ,a_{n})\not =0.} The Cauchy–Davenport theorem, named after Augustin Louis Cauchy and Harold Davenport, asserts that for any prime
Restricted_sumset
American mathematician (born 1940)
problems by solving a suitable Cauchy problem in a Hilbert space was developed. Convergence theorems are proved. Discretization of the Cauchy problem
Alexander_Ramm
Reformulation of general relativity
to Current Research. Wiley. pp. 227–265. Bruhat, Yvonne (1962). "The Cauchy Problem". In Witten, L. (ed.). Gravitation: An Introduction to Current Research
Initial value formulation (general relativity)
Initial_value_formulation_(general_relativity)
American mathematician
Lions on integro-differential equations in the kinetic theory of gases (Cauchy problem for Boltzmann equations) and the plasma physics generalization (Vlasov
Ronald_DiPerna
Integral transform useful in probability theory, physics, and engineering
Matthias; Neubrander, Frank (2002), Vector-Valued Laplace Transforms and Cauchy Problems, Birkhäuser Basel, ISBN 978-3-7643-6549-3 Davies, Brian (2002), Integral
Laplace_transform
Theory of hyperbolic spacetimes
also a global Cauchy orthogonal splitting, thus neatly distinguishing a space slicing from an associated family of observers. A Cauchy surface can possess
Geroch's_splitting_theorem
American award for mathematical analysis
Bressan for: Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem. Oxford Lecture Series in Mathematics and its Applications, 20. Oxford
Bôcher_Memorial_Prize
Area of discrete mathematics
faces of a convex polyhedron was studied and generalized by Augustin-Louis Cauchy and Simon Antoine Jean L'Huilier, and represents the beginning of the branch
Graph_theory
Ordinary differential equation
In mathematics, an Euler–Cauchy equation, also known as a Cauchy–Euler equation, equidimensional equation, or Euler's equation, is a linear ordinary differential
Cauchy–Euler_equation
Equation in fluid dynamics
S2CID 115169288 Himonas, A. Alexandrou; Misiołek, Gerard (2001), "The Cauchy problem for an integrable shallow-water equation", Differential and Integral
Camassa–Holm_equation
Kazakh mathematician
the Solution of the Cauchy Problem for an Infinite System of Partial Differential Equations" (1962) "Multipoint Boundary Value Problem for Differential Equations
Orymbek_Zhautykov
Probability distribution
with a Cauchy distribution, then Y = exp(X) has a log-Cauchy distribution; likewise, if Y has a log-Cauchy distribution, then X = log(Y) has a Cauchy distribution
Log-Cauchy_distribution
Theorem
Matthias; Neubrander, Frank (2001), Vector-valued Laplace Transforms and Cauchy Problems, Birkhauser, ISBN 0-8176-6549-8 Staffans, Olof (2005), Well-posed linear
Hille–Yosida_theorem
1973 treatise by Hawking and Ellis
Significance of Curvature 5. Exact Solutions 6. Causal Structure 7. The Cauchy Problem in General Relativity 8. Space-time Singularities 9. Gravitational Collapse
The Large Scale Structure of Space-Time
The_Large_Scale_Structure_of_Space-Time
Russian mathematician
scientific interests: stabilization of solutions of the Cauchy problem and boundary value problems for parabolic equations; qualitative theory of partial
Vasily_Denisov
Venezuelan mathematician (born 1952)
Luis Vega: Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis (2004), "The Cauchy problem for quasi-linear Schrödinger equations", Inventiones Mathematicae, 158
Gustavo_Ponce
Japanese mathematician
first studied the local and global uniqueness of the solutions of the Cauchy problem for partial differential equations. While at the Courant Institute of
Hitoshi_Kumano-Go
Functional equation
Cauchy's functional equation is the functional equation: f ( x + y ) = f ( x ) + f ( y ) . {\displaystyle f(x+y)=f(x)+f(y).} A function f {\displaystyle
Cauchy's_functional_equation
President of the Central African Republic since 2016
Faustin. Problème de Cauchy matriciels C∞ et dans les espaces de Sobolev à caractéristiques multiples. Matrix Cauchy problems with multiple characteristics
Faustin-Archange_Touadéra
mathematics. His Ph.D. thesis Some Results on (C0) Semigroups and the Cauchy Problem was supervised by Gilbert Strang . From 1967 to 1971 Packel was an assistant
Edward_W._Packel
Italian mathematician (1922–1996)
tangential Cauchy–Riemann condition, extending a previous result of Francesco Severi: this theorem and the Lewy–Kneser theorem on the local Cauchy problem for
Gaetano_Fichera
Mathematics
solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition
Neumann_boundary_condition
CAUCHY PROBLEM
CAUCHY PROBLEM
Boy/Male
Australian, Norse, Scottish
Relic
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : topographic name for someone who lived by a causeway, Middle English caucey (from Old Norman French cauciée); the ending of the word was in time assimilated by folk etymology to Middle English way.
Female
English
English pet form of French Catharine, CATHY means "pure."
Boy/Male
Irish
Observant; alert; vigorous.
Boy/Male
Irish
Observant; alert; vigorous.
Girl/Female
American, Australian
Storage Place
Girl/Female
Hindu, Indian
Wonderful
Boy/Male
Spanish
Bringer of peace.
Surname or Lastname
Cornish and Welsh
Cornish and Welsh : nickname for a red-haired man, from cough, coch ‘red(-haired)’. Compare Gough.English : metonymic occupational name for a maker of beds or bedding, or perhaps a nickname for a lazy man, from Middle English, Old French couche ‘bed’, a derivative of Old French coucher ‘to lay down’, Latin collocare ‘to place’.
Boy/Male
British, English
Good with Bow and Arrow; A Diminutive of Archibald; True and Bold
Male
Spanish
Pet form of Spanish Jesús, CHUCHO means "God is salvation."
Boy/Male
Scottish English
True and bold. Also 'bald'. Introduced from England and Germany during the Norman conquest, the...
Girl/Female
Greek American French Latin Irish English
Form of the Greek Catherine meaning 'pure'.
Boy/Male
American, Australian, German
Man
Surname or Lastname
English
English : perhaps a variant spelling of Cosby.
Girl/Female
Native American
To catch up with.
Surname or Lastname
English
English : occupational name for a maker of beds or bedding, from Middle English couche ‘bed’ (see Couch) + man.
Girl/Female
Arabic
Going Up
Girl/Female
American, Assamese, Christian, English, German, Greek, Indian, Italian, Kannada, Latin, Marathi, Swedish
Pure
Girl/Female
Irish
Vigilant.
CAUCHY PROBLEM
CAUCHY PROBLEM
Boy/Male
Australian, Danish, Finnish, French, German, Norse, Norwegian, Scandinavian, Swedish, Swiss
Strong Counselor; Deciding Warrior; Powerful Army
Boy/Male
Teutonic American English Irish
Guard.
Girl/Female
Tamil
Timid
Boy/Male
Latin Dutch German Hungarian
Hammer.
Surname or Lastname
English
English : unexplained.Italian (Venice and Mantua) and Greek (Zanes) : from a variant of the Venetian personal name Z(u)an(n)i ‘John’ (see Zani).Americanized spelling of German and Jewish Zahn.Robert Zane was a cloth maker of English origin, a founding member of the Quaker colony that was set up at Salem, NJ, in 1676.
Girl/Female
Hindu, Indian, Tamil
Donate
Surname or Lastname
Czech and Slovak (Bareš)
Czech and Slovak (Bareš) : from a pet form of the personal name Bartoloměj (see Bartholomew).German : probably from a Germanic personal name based on bero ‘bear’English : unexplained; perhaps a variant of Barrs or Barras.Galician : habitational name from Bares in A Coruña province.
Boy/Male
English American
and Zachary.
Boy/Male
Hindu, Indian, Traditional
Victorious Lord Shiva
Boy/Male
Tamil
Nityagopal | நிதà¯à®¯à®•à¯‹à®ªà®¾à®²Â
Constant
CAUCHY PROBLEM
CAUCHY PROBLEM
CAUCHY PROBLEM
CAUCHY PROBLEM
CAUCHY PROBLEM
imp. & p. p.
of Catch
v. t.
To take or receive; esp. to take by sympathy, contagion, infection, or exposure; as, to catch the spirit of an occasion; to catch the measles or smallpox; to catch cold; the house caught fire.
v. t.
To seize with the senses or the mind; to apprehend; as, to catch a melody.
v. t.
To seize after pursuing; to arrest; as, to catch a thief.
n.
That by which anything is caught or temporarily fastened; as, the catch of a gate.
n.
That which is caught or taken; profit; gain; especially, the whole quantity caught or taken at one time; as, a good catch of fish.
superl.
Showing impertinent boldness or pertness; transgressing the rules of decorum; treating superiors with contempt; impudent; insolent; as, a saucy fellow.
v. i.
To take hold; as, the bolt does not catch.
v. t.
To reach in time; to come up with; as, to catch a train.
v. i.
To hold, or meet in, a caucus or caucuses.
v. t.
Lying on its side; thus, a chevron couche is one which emerges from one side of the escutcheon and has its apex on the opposite side, or at the fess point.
v. t.
To treat by pushing down or displacing the opaque lens with a needle; as, to couch a cataract.
v. t.
To come upon unexpectedly or by surprise; to find; as, to catch one in the act of stealing.
superl.
Expressive of, or characterized by, impudence; impertinent; as, a saucy eye; saucy looks.
a.
Arched; as, archy brows.
n.
A small species of agouti (Dasyprocta acouchy).
n.
A humorous canon or round, so contrived that the singers catch up each other's words.
n.
Something desirable to be caught, esp. a husband or wife in matrimony.
v. t.
To communicate to; to fasten upon; as, the fire caught the adjoining building.